This study aimed to improve the dispersion state of single-walled carbon nanotubes (SWCNTs) in a cyclo-olefin polymer (COP) matrix by introducing extensional flow during the compounding through a twin-screw extruder (TSE). A modified mixing element with multiple holes, called a fixed blister disc (XBD), was developed. To describe the mixing performance of XBD, the flow state was characterized via numerical simulation and acquisition of process data such as pressure drop (ΔP) at XBD and specific mechanical energy (SME), while the operational conditions of TSE were varied. The dispersion state of SWCNTs was evaluated from the viewpoint of the melt viscoelastic property, surface resistivity of extruded samples and mechanical properties of injection molded samples. Furthermore, the dispersion morphology was observed via optical microscopy and scanning electron microscopy. As a result, the mixing performance of XBD was improved by increasing the ratio of throughputs Q to screw speed N s (Q/N s ) since ΔP, which is related to extensional stress, was increased. However, the trade-off relationship between ΔP and SME was confirmed versus Q/N s . Although the dispersion state at the submicron level was markedly improved with higher SME inputs, higher ΔP reduced the largest agglomerate size and improved dispersion uniformity. Consequently, the mechanical properties were improved significantly.